At present, a number of second-generation dynamic spectrum management, DSM level2, algorithms exist, such as optimum spectrum balancing, OSB, iterative water-filling, IWF, and Iterative spectrum balancing, ISB. With the DSM level2 algorithm, a transmitting power spectral density, PSD, of each subscriber line that makes the overall PSD optimal can be obtained. The DSM level2 algorithm is based on an assumption that all subscriber lines are activated at the same time; however, if multiple subscribers are activated dynamically, that is, the activations of various subscriber lines are performed in a certain sequence, PSD obtained through this algorithm tends to match poorly. For example, for a first activated subscriber line, since it is not affected by the crosstalk of the other activated subscriber lines or only affected by the crosstalk of some of the other activated subscriber lines, the noise floor level of it is relatively slow. The subscriber line uses the existing water-filling algorithm to perform bit loading. According to bit loading formula:
      b    k    n    =            log      2        (          1      +                                                                                h                k                                  n                  ,                  n                                                                    2                    ⁢                      s            k            n                                                              ∑                              m                ≠                n                                      ⁢                                                  ⁢                                                                                                  h                    k                                          n                      ,                      m                                                                                        2                            ⁢                              s                k                m                                              +                      σ            k            n                                )  The obtained bkn will be larger obviously. The reflected effect is that the activation rate is relatively larger with respect to the management target.
In the formula, bkn represents the number of bit loading for the kth subcarrier of line n, skn and skm respectively represent the transmission power of the kth subcarrier of line n and line m, hkn,n represents the direct channel for the kth subcarrier of line hkn,m represents the crosstalk channel of line m to line n on the kth subcarrier, and σkn represents the silent noise on the kth subcarrier of line n.
With the continuous activation of the remaining subscriber lines, the crosstalk suffered by the activated subscriber lines will increase gradually, that is, the level of their noise floor will increase gradually to a reasonable level. In such case, the number of bits that can be loaded by their channels will be less than that in the activation. The margin of the subscriber line decreases gradually, thus causing instability and even re-activation of the line.
A subscriber line may be activated repeatedly until convergence, due to the presence of margin, this convergence process may be very long, and the subscriber line even needs to be manually activated circularly to achieve a balance state achieving the management target.